论文标题
简单的递归，无参数，明确定义的插值节点
Recursive, parameter-free, explicitly defined interpolation nodes for simplices
论文作者
论文摘要
介绍了单纯性$ n $ th级多项式的插值节点的规则。这些节点易于从1D节点集的家族（例如Lobatto-Gauss-Legendre（LGL）节点）递归定义。由此产生的节点具有吸引人的属性：它们完全对称，它们匹配单纯形边缘上的构造中使用的1D家族，而为$（d-1）$ -SINSELX构建的节点是为$ d $ -simplex构建的节点的边界痕迹。 When compared using the Lebesgue constant to other explicit rules for defining interpolation nodes, the nodes recursively constructed from LGL nodes are nearly as good as the "warp & blend" nodes of Warburton in 2D (which, though defined differently, are very similar), and in 3D are better than other known explicit rules by increasing margins for $n > 6$.通过同一度量，这些递归定义的节点不如通过优化Lebesgue常数或相关函数而发现的隐式定义节点好，但是对于四面体，此类最佳节点集尚未计算。参考Python实现已分发为“递归版”软件包，但是递归结构的简单性使其易于实现。
A rule for constructing interpolation nodes for $n$th degree polynomials on the simplex is presented. These nodes are simple to define recursively from families of 1D node sets, such as the Lobatto-Gauss-Legendre (LGL) nodes. The resulting nodes have attractive properties: they are fully symmetric, they match the 1D family used in construction on the edges of the simplex, and the nodes constructed for the $(d-1)$-simplex are the boundary traces of the nodes constructed for the $d$-simplex. When compared using the Lebesgue constant to other explicit rules for defining interpolation nodes, the nodes recursively constructed from LGL nodes are nearly as good as the "warp & blend" nodes of Warburton in 2D (which, though defined differently, are very similar), and in 3D are better than other known explicit rules by increasing margins for $n > 6$. By that same measure, these recursively defined nodes are not as good as implicitly defined nodes found by optimizing the Lebesgue constant or related functions, but such optimal node sets have yet to be computed for the tetrahedron. A reference python implementation has been distributed as the `recursivenodes` package, but the simplicity of the recursive construction makes them easy to implement.
